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## Homework Statement

Consider two identical ideal springs with a mass m attached which are harmonically oscillating out of phase relative to each other, with the spring constant k = 100 N/m and the mass m = 1x10-3 kg.

At the time t

_{0}= +0.1 sec, the displacement of the spring 1 is x

_{1}(t

_{0}) = 10 mm and the displacement of spring 2 is x

_{2}(t

_{0}) = 1 mm.

(i) Calculate the value of the amplitude A of each oscillation.

(ii) Calculate the value of the phase-difference ∅ between the two oscillators.

## Homework Equations

ω = [itex]\sqrt{k/m}[/itex]

x = Acos(ωt + ∅)

kA

^{2}= mv

^{2}+ kx

^{2}

## The Attempt at a Solution

So I calculated ω = 316.228 rad/s. In order to find A, I can use either the position equation or the energy equation. But both of these have an unknown variable. I can't seem to figure out how to find one of these. In the case of the equation x = Acos(ωt + ∅), is ∅ included in this as I am given time with the symbol t

_{0}? Any help would really be appreciated. Also for part (ii) of the question, I have never solved a question before asking for the phase difference between two objects. Do you just subtract one from the other? Or is there a specific method?

Thanks